Networks with Customers, Signals, and Product Form Solution

In this chapter we present an overview of the latest developments in queueing networks with product form stationary distributions. Under a general framework that allows instantaneous movements, we present sufficient conditions for the network to possess a product form solution. For the case where transitions can involve at most two nodes, we present necessary and sufficient conditions for the network to have a product form solution.

[1]  J. R. Jackson.  Networks of Waiting Lines , 1957 .

[2]  P. Whittle.  Equilibrium distributions for an open migration process , 1968, Journal of Applied Probability.

[3]  J. Kingman.  Markov population processes , 1969, Journal of Applied Probability.

[4]  Frank Kelly,et al.  Networks of queues with customers of different types , 1975, Journal of Applied Probability.

[5]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[6]  F. Kelly,et al.  Networks of queues , 1976, Advances in Applied Probability.

[7]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[8]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[9]  Frank Kelly,et al.  Networks of Quasi-Reversible Nodes , 1982 .

[10]  Hans Daduna,et al.  Networks of queues in discrete time , 1983, Z. Oper. Research.

[11]  Peter Whittle,et al.  Systems in stochastic equilibrium , 1986 .

[12]  P. Pollett.  Connecting reversible Markov processes , 1986, Advances in Applied Probability.

[13]  Ruth J. Williams,et al.  Brownian Models of Open Queueing Networks with Homogeneous Customer Populations , 1987 .

[14]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[15]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[16]  R. Serfozo.  Poisson functionals of Markov processes and queueing networks , 1989 .

[17]  E. Gelenbe.  Product-form queueing networks with negative and positive customers , 1991 .

[18]  Yu. V. Malinkovskii.  Criterion for pointwise independence of states of units in an open stationary Markov queueing network with one class of customers , 1991 .

[19]  J. M. Harrison,et al.  Brownian Models of Feedforward Queueing Networks: Quasireversibility and Product Form Solutions , 1992 .

[20]  Nico M. van Dijk.  Queueing networks and product forms - a systems approach , 1993, Wiley-Interscience series in systems and optimization.

[21]  Roy D. Yates.  Analysis of discrete time queues via the reversed process , 1994, Queueing Syst. Theory Appl..

[22]  Xiuli Chao,et al.  Networks of Queues with Customers, Signals and Arbitrary Service Time Distributions , 1995, Oper. Res..

[23]  Michael Pinedo,et al.  On Queueing Networks with Signals and History-Dependent Routing , 1995, Probability in the Engineering and Informational Sciences.

[24]  Michael Pinedo,et al.  Networks of queues with batch services, signals and product form solutions , 1995, Oper. Res. Lett..

[25]  Michael Pinedo,et al.  Networks of queues with batch services and customer coalescence , 1996 .

[26]  X. Chao.  PARTIAL BALANCES IN BATCH ARRIVAL BATCH SERVICE AND ASSEMBLE-TRANSFER QUEUEING NETWORKS , 1997 .

[27]  Xiuli Chao,et al.  A result on networks of queues with customer coalescence and state-dependent signaling , 1998 .

[28]  Masakiyo Miyazawa,et al.  Markov network processes with product form stationary distributions , 1998, Queueing Syst. Theory Appl..

[29]  Masakiyo Miyazawa,et al.  On Quasi-Reversibility and Local Balance: An Alternative Derivation of the Product-Form Results , 1998, Oper. Res..

[30]  R. Serfozo.  Introduction to Stochastic Networks , 1999 .

[31]  Michael Pinedo,et al.  Queueing networks - customers, signals and product form solutions , 1999, Wiley-Interscience series in systems and optimization.

[32]  Xiuli Chao,et al.  Triggered Concurrent Batch Arrivals and Batch Departures in Queueing Networks , 2000, Discret. Event Dyn. Syst..

[33]  Masakiyo Miyazawa,et al.  Queueing networks with instantaneous movements: a unified approach by quasi-reversibility , 2000, Advances in Applied Probability.

[34]  Masakiyo Miyazawa,et al.  ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS , 2000, Probability in the Engineering and Informational Sciences.

[35]  Xiuli Chao,et al.  Queueing networks with string transitions of mixed vector additions and vector removals , 2001 .

[36]  Hans Daduna.  Queueing networks with discrete time scale: explicit expressions for the steady state behavior of discrete time stochastic networks , 2001 .

[37]  Richard J. Boucherie,et al.  Arrival first queueing networks with applications in kanban production systems , 2003, Perform. Evaluation.

[38]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[39]  Thomas Bonald,et al.  On Kelly networks with shuffling , 2008, Queueing Syst. Theory Appl..